Coded-wavelength multiplex volume holography

ABSTRACT

A method for coded-wavelength multiplexing according to which a signal waves S i  (r) is recorded in a holographic medium in a counter-propagating geometry using corresponding writing reference waves R i  (r). The method involves selecting discrete wavelengths λ and encoding reference wave vectors ρ l  which make up writing reference waves R i  (r) such that the writing reference waves R i  (r) at each wavelength λ are orthogonal. The stored signal waves S i  (r) are reconstructed in the form of reconstruction waves A c  (σ) with reconstruction reference waves R c  (r) selected from among the writing reference waves R i  (r). In the event of angular multiplexing of the reference wave vectors ρ l , it is possible to use one reference wave to produce a number of reconstruction waves A c  (σ) and generate a mosaic of desired holographic pages.

This invention was made with U.S. Government support under Grant No.MDA972-94-2-0008 awarded by ARPA. The U.S. Government has certain rightsin this invention.

This application is a continuing application of application No.08/643,062 filed Apr. 30, 1996, now abandoned.

BACKGROUND--FIELD OF THE INVENTION

The present invention relates to the field of holographic data storage,and in particular to a method for coded-wavelength multiplexing forstoring and reconstructing signals in a holographic recording medium.

BACKGROUND--DESCRIPTION OF PRIOR ART

Volume holographic data storage and processing offer the potential forhandling large quantities of data given the inherent high capacity ofbulk media. Optical addressing ensures fast access times and theparallel nature of the medium translates into fast transfer rates.Capacity is governed by the numerical aperture of the signal, the numberof holograms, or pages, the volume of the medium, and the acceptablelevel of cross talk and other noise sources.

It is well-known, that multiple holograms can be stored in the samevolume using various encoding methods. Typically, in a volume Fourierholographic arrangement, these methods are based on angle, wavelength,or phase encoding. They can be practiced in either propagating orcounter-propagating geometries. Thorough discussions of thesearrangements can be found in the literature.

The efforts to store more holographic pages in a holographic recordingmedium are most often thwarted by increasing cross talk. Consequently,there is great interest in developing arrangements and methods forreducing this noise source. George A. Rakuljic et al. in their articleentitled "Optical Data Storage by Using Orthogonal Wavelength-MultiplexVolume Holograms" appearing in Optics Letters, Oct. 15, 1992, Vol. 17,No. 20, pp. 1471-3 discuss how to reduce holographic cross talk in asimple wavelength multiplexed system. In particular, improveddifferentiation of wavelength-multiplexed holographic pages is predictedfor a holographic system using counter-propagating signal and referencebeams. The success of the method hinges on identifying proper regions inK-space, which is the space of hologram grating vectors representingstored data, where the necessary separation Δk, which is the change inwavelength or mismatch required to minimize cross talk betweenreconstructions of the desired holographic page and the adjacentholographic page, is minimum. Appropriate wavelength multiplexing canensure this result when the information is distributed uniformly inK-space. This reduces cross talk in comparison to conventionalarrangements relying on angular multiplexing and permits one to storemore holographic pages.

Further improvements in holographic storage are desirable. Inparticular, it would be advantageous to increase the capacity of theconstrained holographic system by increasing the number of pages whichcan be stored. Increased flexibility in the manner the holographic pagesare stored and reconstructed would be advantageous in all applications,including: optical information storage, optical computing, neuralnetworks, associative memory, and other uses. A multiplexing methodwhich would satisfy these requirements would greatly enhance thepotential of holography to gain widespread acceptance for data storageand processing.

OBJECTS AND ADVANTAGES OF THE INVENTION

In view of the above shortcomings of prior art, it is an object of thepresent invention to provide a method for practicing coded-wavelengthmultiplex holography in a counter-propagating geometry which enables theuser to store an increased number of holographic pages in a holographicrecording medium. Thus, the capacity of the holographic system isincreased.

It is another object of the invention to provide a multiplexing methodfor holography which makes it possible to spatially separate theundesired cross talk from the reconstructed signal when practicingcoded-wavelength multiplex holography in conjunction with angularmultiplexing.

Yet another object of the invention is to adapt the method of theinvention to permit the use of the cross talk signal for expanding thesize of a holographic page in conjunction with angular multiplexing.This method will create a mosaic of holographic pages.

It is yet another object of the invention to ensure that the method canbe practiced using simple and easy-to-control optical elements andsystems.

These and other objects and advantages will become more apparent afterconsideration of the ensuing description and the accompanying drawings.

SUMMARY OF THE INVENTION

The objects and advantages of the invention are ensured by a uniquemethod of multiplexing data in a holographic recording medium. This newtechnique is best described as coded-wavelength multiplexing and it isbased on writing a signal wave S_(i) (r) with a corresponding writingreference wave R_(i) (r) in a counter-propagating geometry. The methodinvolves the steps of selecting a wavelength λ at which the signal waveS_(i) (r) bearing either digital or analog information will be stored inthe medium. The writing reference wave R_(i) (r) is also set to thisselected wavelength λ.

A first signal wave S₁ (r) having a spectrum of wave vectors representedby a representative signal wave vector σ is then generated at wavelengthλ. Also generated at wavelength λ is a first writing reference wave R₁(r). The first writing reference wave R₁ (r) has a number n of referencewave vectors ρ_(l), where l=1 . . . n and n is at least 1. The firstsignal wave S₁ (r) is written or recorded in the holographic medium withthe first writing reference wave R₁ (r) according to generally knownprinciples of holography. A second signal wave S₂ (r) having therepresentative signal wave vector σ and a second writing reference waveR₂ (r) are generated at the same frequency λ to record the second signalS₂ (r) in the holographic medium. Again, second writing reference waveR₂ (r) is made up of a number m of reference wave vectors ρ_(l), wherel=1 . . . m and m is at least 1. The reference wave vectors p_(l) forboth the first writing reference wave R₁ (r) and for the second writingreference wave R₂ (r) are selected in such a way as to render these twowaves orthogonal.

The orthogonality of the first and second writing reference waves isensured by properly coding the reference wave vectors ρ_(l). Inparticular, angular and phase-encoded multiplexing can be used togenerate sets of reference wave vectors which produce orthogonal writingreference beams. In the event of angular multiplexing the number ofreference wave vectors ρ_(l) required for each writing reference beam is1 (m=n=1). For phase-encoded multiplexing each writing reference beamwill have at least two reference wave vectors ρ_(l) (m≧2; n≧2). Forpractical reasons, it is preferable that number of reference wavevectors ρ_(l) be the same for both writing reference waves (m=n). Inphase-encoded multiplexing individual reference wave vectors ρ_(l) areassigned different phases. Preferably, the reference wave vectors areassigned Walsh-Hadamard binary codes.

The stored first signal wave S₁ (r) is reconstructed or recalled with areconstruction reference wave R_(c) (r) selected from among the firstand second writing reference waves. In the event of angular multiplexingof the reference wave vectors ρ_(l) in the counter-propagating geometryit is possible to arrange a system to use either reference wave as thereconstruction reference wave R_(c) (r) to reconstruct one or bothsignal waves. The reconstruction reference wave R_(c) (r) produces areconstruction wave A_(c) (σ), which is projected on a detectionmechanism or screen, such as an array of charge-coupled devices (CCDs)or the like. It is preferable that detection mechanism or screen havepixels if the data stored in the holographic medium is digital.

In a preferred embodiment the signal wave S_(i) (r) has a limited fieldof view and the reference wave vectors ρ_(l) are angle multiplexed. Inthis instance the method allows one to obtain a first reconstructionwave A₁ (σ) and a second reconstruction wave A₂ (σ) using only the firstwriting reference wave R₁ (r) as the reconstruction reference wave R_(c)(r). In this arrangement the screen can have a spatial extent sufficientto intercept both reconstructed waves. In other words, thereconstructions of both signal waves can be viewed simultaneously. Thelocation of one reconstruction does not overlap the other, thus there isno cross talk between data in the two reconstructions.

Of course, angular and phase-encoded multiplexing of the reference wavevectors ρ_(l) can be implemented in the same arrangement. Also, themethod of the invention can be extended in a straightforward manner tostore and reconstruct any large number of signal waves S_(i) (r). To dothis the number of writing reference beams R_(i) (r) can be larger than2. Also, the same steps can be repeated at many wavelengths. Inparticular, it is preferable that λ be selected from a spectrum ofdiscrete wavelengths.

Another particularly advantageous effect of the invention, whenassigning different angles (angle coding) the reference wave vectorsp_(l) is the ability to generate a mosaic of reconstructed waves A_(c)(σ). To do this the imaging screen has to be sufficiently large tointercept a select number or all reconstructions at a particularwavelength, e.g., λ₁. In practice, the mosaic concept presents a veryattractive way of taking advantage of cross-talk reconstructions to viewmultiple holographic pages simultaneously.

The details of the invention are presented in the below description,which clarifies the various aspects of the invention in reference to theattached drawing figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an isometric view showing a counter-propagating geometricalarrangement for practicing the method of the invention.

FIG. 2 is a top view of the arrangement of FIG. 1.

FIG. 3 is a diagram depicting wave vector degeneracy for angular codingof reference wave vectors ρ_(l).

FIG. 4 is a diagram depicting the projection of two reconstructed signalbeams having limited fields of view.

FIG. 5 is a front view of the imaging screen of FIG. 4.

FIG. 6 is a diagram depicting the angular dimensions of a limited fieldof view of a signal beam.

FIG. 7 is an isometric view illustrating coded reference wave vectorswhich have mutually orthogonal angles.

FIG. 8 is a diagram illustrating the recording of three signal wavesS_(i) (r).

FIG. 9 is a diagram illustrating the reconstruction of the three signalbeams recorded according to FIG. 8.

FIG. 10 is a diagram showing the dephasing parameter for angular codingof reference wave vectors ρ_(l).

FIG. 11 is a diagram visualizing the dephasing condition for differentwavelengths λ selected from a spectrum.

FIG. 12 is a view of a mosaic arrangement produced with the methodaccording to the invention.

DESCRIPTION

The method of the invention will be best understood by first reviewingthe counter-propagating geometry as illustrated in FIG. 1. A holographicarrangement 10 has a holographic recording medium 12 centrallypositioned between a reference beam arm 14 and a signal beam arm 16.Medium 12 can be made of any bulk holographic material or stratifiedholographic medium, which may be photorefractive or otherwise capable ofpreserving local changes of the index of refraction as a result ofincident radiation.

In reference arm 14 a writing reference beam or wave R_(i) (r) is shapedand guided by conventional optical elements. The optical elementsinclude a deflector 18, a collimating lens 20 or a Phase Spatial LightModulator 34 (PSLM), a Fourier or focusing lens 22, and a beam splitteror half-silvered mirror 24. Both lens 20 and PSLM 34 are drawn in dottedlines because the choice between them depends on whether angular orphase multiplexing will be practiced. As is well-known, no PSLM 34 isrequired for angular multiplexing and for phase multiplexing lens 20 isnot necessary.

Deflector 18 has adjustable tilt for steering writing reference waveR_(i) (r). This is indicated by arrow T. In particular, deflection ofwriting reference wave R_(i) (r) changes the angle of incidence of waveR_(i) (r) on medium 12 and allows for angular multiplexing, as explainedbelow.

The mechanism for producing the tilt is not shown. In fact, any knownmethod of deflecting writing reference wave R_(i) (r) can be utilized bydeflector 18, e.g., the electro-optic or acousto-optic effect.Collimating lens 20 shapes writing reference wave R_(i) (r) and focusinglens 22 focuses it on medium 12.

A Phase Spatial Light Modulator 34 (PSLM) is positioned in the path ofwriting reference wave R_(i) (r). PSLM 34 alters the phase of portionsof reference wave vectors ρ_(l), where l=1 . . . n, which make upwriting reference wave R_(i) (r). According to the theory of holographicstorage, a reference beam can be regarded as a collection of planewaves. Each of these plane waves is designated by one reference wavevector ρ_(l). In the absence of PSLM 34 reference wave R_(i) (r)consists of only one plane wave and is thus described by one referencewave vector ρ₁, i.e., n=1. With PSLM 34 in place the maximum number n ofreference wave vectors ρ_(l) corresponds to the number of pixels of PSLM34. In other words, each plane wave designated by reference wave vectorρ_(l) is associated with a pixel of PSLM 34. Beam splitter 24 is used tofilter out and direct out of reference arm 14 a reconstruction beam orwave A_(c) (σ), as described below.

Holographic arrangement 10 is designed for operating with pages ofholographic data. Consequently, signal beam arm 16 is equipped with aSpatial Light Modulator 26 (SLM) for producing holographic pages. As iswell-known in the art, other elements for impressing data or any objectto be stored in medium 12 can be placed at the location of SLM 26.

Signal wave S_(i) (r) passes through SLM 26 and arrives at a focusinglens 28, which focuses it on medium 12. There wave S_(i) (r) is storedwith corresponding writing reference wave R_(i) (r). Reconstruction ofstored wave S_(i) (r) is performed with a reconstruction reference waveR_(c) (r). The latter can be the same as writing reference wave R_(i)(r) with which wave S_(i) (r) was originally stored, or, according tothe present method, with a difference reference wave R_(i) (r). Thisoperation yields reconstruction wave A_(c) (σ), which is deflected outof the reference beam arm 14 by beam splitter 24. A collimating lens 30shapes reconstruction wave A_(c) (σ) and projects it onto a detectionunit, imaging screen or CCD 32. Any screen or device can be used tovisualize, read, or record the data carried by reconstruction wave A_(c)(σ).

The top view in FIG. 2 better depicts arrangement 10 by indicating howreference wave R_(i) (r) and signal wave S_(i) (r) are shaped by theoptical elements. Also, FIG. 2 illustrates how the operation of PSLM 34and lens 20 (and deflector 18) are interchangeable. Changing a tiltangle ω of deflector 18 can redirect reference wave R_(i) (r). Thus,deflector 18 permits the user to practice angular multiplexing. In thiscase only one plane wave front corresponding to one reference wavevector p_(l) constitutes reference wave R_(i) (r). Meanwhile, PSLM 34can impart a different phase to portions of reference wave R_(i) (r)thus creating corresponding reference wave vectors ρ_(l) of wave R_(i)(r). This enables one to perform phase multiplexing. Phase is practicedwhen PSLM 34 is used, and angle multiplexing requires lens 20 withdeflector 18. In special cases, PSLM 34 by itself can act as a deflectorby only allowing reference wave vectors ρ_(l) of certain pixels to pass.This solution may be practical in some arrangements. The importantaspect to practicing the method of the invention is that either angular,or phase, or both types of multiplexing be possible with arrangement 10.A person skilled in the art will be able to select the appropriateoptical elements based on experience and the present disclosure.

As shown in FIG. 2, deflector 18 steers reference wave R_(i) (r) over asteering angle ω. Although in the figure ω only denotes the angularcomponent in the y-z plane, it is understood that steering angle ωvaries in three dimensional space. In fact, for the purposes of thisdiscussion, all other angles used below are assumed to vary in threedimensions unless otherwise indicated. As expected, a change in steeringangle ω causes reference wave R_(i) (r) to impinge on medium 12 at anangle of incidence equal to steering angle ω (see FIG. 7). This will beexplained in more detail below in discussing the preferred embodiment.

Focusing lens 22 converges reference wave R_(i) (r) and directs it atmedium 12. Analogously, lens 28 focuses signal wave S_(i) (r) on a faceof medium 12. Reconstructed wave A_(c) (σ) is collimated by lens 30,after deflection out of reference arm 14 by beam splitter 24, andprojected on imaging screen 32.

A particular wavelength λ of light is first selected for reference waveR_(i) (r) and signal wave S_(i) (r). Once signal wave S_(i) (r) isgenerated, wavelength λ determines a representative signal wave vector σaccording to well-known physical principles (|σ|=2π/λ). It is understoodthat representative signal wave vector σ represents a central orotherwise representative signal wave vector which stands for acontinuous or discrete number of wave vectors actually constitutingsignal wave S_(i) (r). Analogously, wavelength λ dictates the magnitudeof reference wave vectors ρ_(l) making up reference wave R_(i) (r).These vectors and their relationships are essential to the understandingof the invention.

To better analyze the situation, both reference wave R_(i) (r) andsignal wave S_(i) (r) are Fourier transformed. In this manner theirsignal and reference wave vectors ρ_(l) and σ can be represented in thereciprocal space or K-space. By using the standard Fouriertransformation one obtains the following complex amplitudes for wavesR_(i) (r) and S_(i) (r):

    S.sub.i (r)=∫S.sub.i (σ) exp (iσ·r)d.sup.3 .sigma.

    R.sub.i (r)=Σ.sub.l R.sub.il exp (iρ.sub.l ·r).

Thus, a two-dimensional reciprocal space can be defined as illustratedin FIG. 3. In this space signal wave S_(i) (r) is represented by itssignal wave vector σ and reference wave R_(i) (r) by its reference wavevector ρ. For simplicity, it is assumed that n=1 and thus only onereference wave vector ρ_(l) =ρ makes up each reference wave (nophase-encoded multiplexing). For better understanding, the axes K_(y)and K_(z) correspond to those labeled in FIG. 2. The diagram shows thegrating vector K written in medium 12 by signal wave vector σ andreference wave vector ρ. In fact, the Ewald circle denoted by L1, is thelocus of all grating vectors which can be written with reference wavevector ρ. In all cases, grating vector K is calculated from theequation:

    K=σ-ρ

As illustrated, grating vector K produced by the pair of vectors σ and ρcan also be obtained with wave vectors -σ and -ρ. In other words, wavevectors σ and ρ are degenerate to the wave vector pair -σ and -ρ, sincegrating vector K belongs to locus L1 and locus L2 of all grating vectorswhich can be written using wave vector -σ as the reference wave vector.This also means that signal wave vector σ recorded with reference wavevector ρ can be recalled using wave vector -σ as an alternativereference wave vector.

When wave vector -σ is used as the reference wave vector, however, wavevector -ρ will also be reconstructed, if it was previously recorded.Therefore, in a situation where both vectors σ and -ρ have been recordedin medium 12, using reference wave vector ρ and vector -σ respectively,their reconstructions are generated simultaneously. In this case angleoff incidence α--equal to angle ω--of reference wave vector -σ used inwriting wave vector -ρ was equal to 0. Consequently, reconstructions ofwave vectors σ and -ρ will emanate along the dotted lines offset fromeach other by angle of incidence α.

FIG. 4 affords a detailed view of reconstruction waves A_(c) (σ) andA_(c) (-ρ) corresponding to wave vectors σ and -ρ. A grating spectrum 50corresponding to wave vector -ρ and a grating spectrum 52 correspondingto wave vector σ are indicated on Ewald circles L1 and L2 respectively.

Grating spectra 50 and 52 are related to the fields of view of wavesA_(c) (σ) and A_(c) (-ρ) and are quasi-Bragg matched. Under thesecircumstances, the field of view for wave A_(c) (σ), for example, isgoverned by the condition that σ+δσ has to yield Δk_(z) =2π/L, where Lis the characteristic interaction length of waves R_(i) (r) and S_(i)(r). Typically, the interaction length L is the smaller of the length ofmedium 12 or coherence length of the laser light used in waves R_(i) (r)and S_(i) (r).

In fact Δk_(z) =2π/L determines the first null at which allreconstruction will disappear. For all practical purposes the nullposition is construed as the outer limit or border of reconstructionwave A_(c) (σ). Because of the symmetry of the problem, the field ofview is equal to: ##EQU1##

The fields of view of reconstruction waves A_(c) (σ) and A_(c) (-ρ) arecalculated using this equation. This is done to determine the minimumangle αρ of reference wave vector ρ directly related to angle ω, whichwill ensure that reconstruction waves A_(c) (σ) and A_(c) (-ρ) areresolved on screen 32. In other words, to avoid overlap ofreconstruction waves A_(c) (σ) and A_(c) (-ρ) the spatial extent ofthese reconstructions is calculated a priori and made sufficiently smallto ensure that, propagating at an angular offset equal to angle ofincidence α, the projections of waves A_(c) (σ) and A_(c) (-ρ) do notoverlap on screen 32. In FIG. 4 angle α is so large that reconstructionwave A_(c) (-ρ) is not intercepted by screen 32 at all.

Technically, when viewing one of the reconstructed waves, e.g., waveA_(c) (σ), the second wave, in this case A_(c) (-ρ), represents crosstalk. Thus, in accordance with the method of the invention, with the aidof angular multiplexing cross talk is spatially separated from thedesired signal. This is visualized in FIG. 5 where the reconstructionswave A_(c) (σ) is shown to project on screen 32 and undesiredreconstruction wave A_(c) (-ρ) misses screen 32. For example purposes,the information carried by waves A_(c) (σ) and A_(c) (-ρ) is assumed tobe in digital form as indicated by the patterns. Of course, theinformation content and form can be entirely arbitrary.

Reconstruction waves A_(c) (σ) and A_(c) (-ρ) each have a limiting orfinite field of view 60 and 62 imposed by the Bragg condition. Fields ofview 60 and 62 are calculated as indicated above from angle αρ andinteraction length L. In practice, any intervening optical system, inthis case collimating lens 30 of FIG. 1, placed in the path of wavesA_(c) (σ) and A_(c) (-ρ) will affect the final size of fields of view 60and 62. A person skilled in the art will be able to select proper systemparameters to ensure that reconstructed beams 54 and 56 are resolved onscreen 32.

In practice, the field of view is further limited by choice of referencewave vectors. In the case of FIG. 1 and FIG. 2 signal wave S_(i) (r) hasa field of view 64 defined in terms of angle of incidence a of referencewave R_(i) (r) or its reference wave vector ρ. This is better shown inFIG. 6. In particular, Δα_(x) is the change along the x direction (intothe page) of reference wave R_(i) (r) between focusing lens 22 andmedium 12. Similarly, Δα_(y) is the change which wave R_(i) (r)experiences along the y direction (same as K_(y)) on the same path. Theallowable field of view 64 can be adjusted by changing the components ofangle α. The general rule for selecting angles of the reference andsignal wave vectors is a given direction can be stated as follows:

    Δθ.sub.92 ≧Δθ.sub.94 =2 Δθ.sub.phalf.

Following the above directions one can determine proper angle ofincidence α for a number of wave vectors ρ_(l) constituting waves R_(i)(r) so that reconstructed waves A_(c) (σ) will not overlap on screen 32.Such waves R_(i) (r) are defined to be orthogonal to each other.

In addition to angle multiplexing, wave vectors ρ_(l) can also be phasemultiplexed. This is done in the usual manner using PSLM 34. The phasecodes of vectors ρ_(l) for each reference wave R_(i) (r) are selectedsuch that waves R_(i) (r) are orthogonal to each other. TheWalsh-Hadamard binary phase codes are particularly suitable for thispurpose. An in-depth discussion of these codes can be found in U.S. Pat.No. 3,612,641 issued to Eaglesfield.

PREFERRED EMBODIMENT

The preferred embodiment uses holographic arrangement 10 shown in FIGS.1 and 2 and applies the above novel principle to a new method ofcoded-wavelength multiplexing in which wave vectors ρ_(l) of individualwaves R_(i) (r) are angle-coded or angle multiplexed. To do this aparticular wavelength λ is first selected for waves R_(i) (r) and S_(i)(r). This wavelength determines the magnitude of the k-vectors.

As an example of the preferred method, FIG. 7 shows three referencewaves R₁ (r), R₂ (r) and R₃ (r) each consisting of a single wave vectorρ. The difference in angle between waves R₁ (r), R₂ (r) and R₃ (r) isequal to tilt angle ω. Thus, waves R₁ (r), R₂ (r) and R₃ (r) areincident on medium 12 at angles α, 0, and -σ. These angles have beencalculated such that reconstructed waves A_(c) (σ) of signals wavesS_(i) (r) will not overlap on screen 32. Thus, reference waves R₁ (r),R₂ (r) and R₃ (r) are mutually orthogonal.

In a first step signal wave S₁ (r) is written in medium 12 using writingreference wave R₁ (r). In a second step wave S₂ (r) is recorded withwave R₂ (r), and then wave S₃ (r) is stored with wave R₃ (r). FIG. 8shows the recorded waves representing them by the corresponding wavevectors. Thus, signal waves S₁ (r), S₂ (r) and S₃ (r) are represented bycorresponding to representative signal wave vectors σ₁, σ₂, σ₃, andwriting reference waves R₁ (r), R₂ (r) and R₃ (r) are indicated by theircorresponding reference wave vectors ρ₁, ρ₂, ρ₃.

The reconstruction of all three signal waves S₁ (r) S₂ (r), S₃ (r) inthis case can be performed with just one reconstruction wave R_(c) (r)selected from among reference waves R₁ (r), R₂ (r) and R₃ (r). In thiscase R_(c) (r) corresponds to R₂ (r), or ρ₂. This is illustrated in FIG.9, where reconstructed waves A₁ (σ), A₂ (σ) and A₃ (σ) are shownpropagating toward screen 32 along the dashed lines.

Cross talk represented by vectors C₁ and C₃ is also reconstructed byvector ρ₂. This is due to the degeneracy condition explained above.Fortunately, vectors C₁ and C₃ propagate at angles α and -α. Thus, thecross talk signals diverge away from the desired reconstruction waves A₁(σ), A₂ (σ) and A₃ (σ). In a particularly preferred embodiment the sizeof screen 32 and its orientation is set so that it intercepts thedesired beams only, i.e., reconstruction waves A₁ (σ) , A₂ (σ) and A₃(σ).

An important feature of the above method of multiplexing according tothe invention allows one to write a signal wave with one reference wavevector and reconstruct it with another. Thus, when practicingcoded-wavelength multiplex holography in conjunction with angularmultiplexing the undesired cross talk is shifted away from screen 32. Ingeneral, the method can be practiced in the counter-propagating geometrywith any number of reference waves R_(i) (r), where i=1 . . . n and n isat least 2 (n≧2). Appropriate reconstruction waves R_(c) (r) are chosenfrom among writing reference waves R_(i) (r). In this manner manyholographic pages can be stored at one particular wavelength λ, therebyincreasing the storage capacity. Also, the method of the invention makesuse of simple and easy-to-control optical elements and systems.

Arrangement 10 of FIG. 1 and FIG. 2 can be used in practicing the methodof the invention at many distinct wavelengths λ. In other words,reference waves R_(i) (r) can consist of sets of coded reference wavevectors ρ_(l) with different k-vector magnitudes. Preferably, eachwavelength λ at which wavelength coded multiplexing is practiced isselected from a spectrum of discrete wavelengths. The wavelengthsbelonging to this spectrum should be sufficiently different to ensure alarge Bragg mismatch between holograms multiplexed at each particularwavelength λ.

The choice of proper wavelength λ will be better understood by referringto FIG. 10. This K-space diagram shows three different recorded signalwave vectors σ₁, σ₂, and σ₃. The first two have the same wavelength λ₁,and consequently the magnitude of their k-vectors is the same. Signalwave vectors σ₁, σ₂ and any other vector at wavelength λ₁, e.g.,reference wave vector ρ₁, are thus described by locus L1. For angularcoding, the difference between signal wave vectors σ₁, σ₂ is indicatedby a dephasing or offset vector Δρ₁₂. In should be noted that offsetvector Δρ₁₂ is nearly perpendicular to vector σ₁, and thus the dephasingparameter varies to second order with angle of incidence α. Signal wavevector σ₃ has a shorter wavelength λ₂. As a result the magnitude of itsk-vector is larger. The magnitude of the corresponding reference vectorρ₂ is equal to that of wave vector σ₃. For clarity, locus L2 delimitsall vectors at wavelength λ₂. The dephasing or offset vector Δρ₁₃between signal wave vectors σ₁, σ₃ is collinear with vector σ₁ andvaries to first order with wavelength. Thus, coded grating spectrarecorded at wavelengths λ₁ and λ₂ will not overlap and cross talk isattenuated in the ordinary manner. In fact, when selecting a set ofdiscrete wavelengths for coded-wavelength multiplexing the regularrequirement for conventional wavelength multiplexing can be used.According to this criterion, defined in terms of frequencies rather thanwavelengths, the selected frequencies should differ by:

    Δf=c/2nL.

FIG. 11 illustrates grating vectors K₁, K₂, and K₃ recorded at the sameangle of incidence α but at decreasing wavelengths corresponding to lociL₁, L₂, and L₃. Grating vectors K₁, K₂, and K₃ do not overlap and aretherefore non-degenerate. This means that cross talk between theirreconstructions is attenuated in the ordinary manner encountered inwavelength multiplexing.

There is another advantage to coded-wavelength multiplexing in whichreference wave vectors ρ_(l) are angle-coded to ensure orthogonality ofreference waves R_(i) (r). This advantage has to do with the ability toproject multiple reconstruction waves A_(c) (σ) corresponding toindependent holographic pages simultaneously (see FIG. 9) . A pattern ormosaic 78 of the reconstructed holographic pages can be created onscreen 32, as illustrated by FIG. 12.

For purposes of a practical example, arrangement 10 of FIG. 1 is used toproduce mosaic 78 through angular encoding at wavelength λ. In thisspecific case, recording medium 12 is a 2 cm long sample of LiNbO₃. Thesource (not shown in drawing figures) for waves R_(i) (r) and S_(i) (r)was a dye laser pumped by an argon-ion laser operating at ≈615 nm with alinewidth of ≈100 GHz, which is substantially larger than the smallestspacing of 3 GHz permitted by wavelength selectivity in this sample.Screen 32 is a CCD camera. The focal length of lens 28 is ≈300 mm, andthe image spans ≈5 mm, so that reference wave vectors ρ_(l) areseparated by ≈1°.

Four holographic pages 70, 72, 74, and 76 corresponding to four signalwaves S_(i) (r) are recorded in medium 12 using four incidence anglesα₁, α₂, α₃ and α₄ at one wavelength λ. All four pages 70, 72, 74, and 76are reconstructed by projecting their corresponding reconstruction wavesA_(c) (σ) on screen 32 simultaneously with just one reference wave R_(i)(r) serving as the reconstruction reference wave R_(c) (r). Although, inthis case mosaic 78 includes only four pages, it may be larger andinclude any desired number of pages. The optimal shape of the mosaic andsize will be determined the person skilled in the art in adapting themethod of the invention to particular problems. It is understood thatthis example is intended to provide the user with a general idea aboutthe parameters involved in practicing the method of the invention and inno way limits its scope.

In general, the method of the invention can be rigorously stated. Theformalism takes into consideration all possible signal waves S_(i) (r)with their signal wave vectors σ and reference waves R_(i) (r) withtheir coded reference wave vectors ρ_(l). In the most general case thereconstruction amplitude can then be approximated by:

    A.sub.c (σ.sub.195)=Σ.sub.j Σ.sub.l Σ.sub.m R*.sub.jl R.sub.cm B.sub.ml (σ)S.sub.j (σ⊥-Δρ.sub.ml ⊥)

in which

    B.sub.ml (σ)=C exp[ξ.sub.ml (σ)]sinc[ξ.sub.ml (σ)],

and ##EQU2##

In the above, sinc(x)=sin(x)/x, C governs the strength of the hologram.This function also defines the nulls in the reconstruction of ahologram. β is the wave number in the medium, and Δρ_(ml) =ρ_(m) -ρ_(l).Because holograms can only be written with one wavelength λ at a time,the reference codes necessarily have the property R*_(jl) R_(cm) =0 whenβ_(l) ≠β_(m). For orthogonal reference codes, Σ_(l) R* _(jl) R_(cl) =0when i ≠c, so that the sources of cross talk are Bragg mismatchreconstructions at B_(ml). For angular encoding at each wavelength withwave vector ρ_(l), the reference codes are given by R_(il) =R_(o)δ_(il). For phase encoding at each wavelength with wave vectors ρ_(l)the orthogonality condition is determined by the phase codes (e.g.,Walsh-Hadamard binary phase codes).

SUMMARY, RAMIFICATIONS, AND SCOPE

As evident from the above discussion, the present invention can bepracticed in many ways. The essential feature is that orthogonal phaseor angle codes be used for the individual reference wave vectors atevery wavelength.

The mosaic concept can be implemented for faster data access or forcomputational purposes. This is particularly useful in the fields ofoptical computing, storage, and other related applications relying onholography.

Therefore, the scope of the invention should be determined, not byexamples given, but by the appended claims and their legal equivalents.

We claim:
 1. A method of holographically storing and retrievinginformation, said method comprising the following steps:a) generating afirst signal wave S₁ characterized by a first signal wave vector σ₁, b)generating a first reference wave R₁ characterized by a first referencewave vector σ₁, wherein ρ₁ =-σ₁, c) illuminating a holographic mediumwith said first signal wave S₁ and said first reference wave R₁, therebyrecording a first grating in said medium, d) generating a second signalwave S₂ characterized by a second signal wave vector σ₂, wherein σ₂ =σ₁,e) generating a second reference wave R₂ characterized by a secondreference wave vector ρ₂, wherein said second reference wave vector ρ₂makes an angle α with respect to said first reference wave vector ρ₁, f)illuminating said holographic medium with said second signal wave S₂ andsaid second reference wave R₂, thereby recording a second grating insaid medium, g) generating a third signal wave S₃ characterized by athird signal wave vector σ₃, wherein σ₃ =σ₁, h) generating a thirdreference wave R₃ characterized by a third reference wave vector ρ₃,wherein said third reference wave vector ρ₃ makes an angle β withrespect to said first reference wave vector ρ₁, wherein said first,second, and third reference wave vectors ρ₁, ρ₂, and ρ₃ are notcoplanar, and wherein said waves S₁, S₂, S₃, R₁, R₂, and R₃ have thesame wavelength, i) illuminating said holographic medium with said thirdsignal wave S₃ and said third reference wave R₃, thereby recording athird grating in said medium, j) illuminating said holographic mediumwith said first reference wave R₁, thereby generating first, second, andthird reconstructed waves characterized by first, second, and thirdreconstructed wave vectors, respectively, wherein said firstreconstructed wave vector is equal to said first signal wave vector σ₁,said second reconstructed wave vector is equal to the negative of saidsecond reference wave vector ρ₂, and said third reconstructed wavevector is equal to the negative of said third reference wave vector ρ₃.2. The method of claim 1, further comprising the step of projecting saidfirst, second and third reconstructed waves on an imaging means.
 3. Themethod of claim 2, wherein said angles α and β are selected so that saidfirst, second, and third reconstructed waves do not overlap on saidimaging means.
 4. The method of claim 1, further comprising the step ofprojecting said first reconstructed wave on an imaging means, andwherein said angle α is selected so that said second reconstructed wavedoes not intercept said imaging means.
 5. The method of claim 1, whereinsaid first, second, and third signal waves S₁, S₂ and S₃ are impressedwith digital data.
 6. The method of claim 1, wherein said first, second,and third signal waves S₁, S₂, and S₃ are impressed with analog data. 7.A method of holographically storing and retrieving information, saidmethod comprising the following steps:a) generating a first signal waveS₁ characterized by:(i) a first signal wave vector σ₁, and (ii) anangular spread θ, b) generating a first reference wave R₁ characterizedby a first reference wave vector ρ₁, wherein ρ₁ =-σ₁, c) illuminating aholographic medium with said first signal wave S₁ and said firstreference wave R₁, thereby recording a first grating in said medium, d)generating a second signal wave S₂ characterized by a second signal wavevector σ₂, wherein σ₂ =σ₁, e) generating a second reference wave R₂characterized by a second reference wave vector ρ₂, wherein said secondreference wave vector ρ₂ makes an angle α with respect to said firstreference wave vector ρ₁, f) illuminating said holographic medium withsaid second signal wave S₂ and said second reference wave R₂, therebyrecording a second grating in said medium, g) generating a third signalwave S₃ characterized by a third signal wave vector σ₃, wherein σ₃ =σ₁,h) generating a third reference wave R₃ characterized by a thirdreference wave vector ρ₃, wherein said third reference wave vector ρ₃makes an angle β with respect to said first reference wave vector ρ₁,wherein said angles α and β are greater than said angular spread θ;wherein said first, second, and third reference wave vectors ρ₁, ρ₂, andρ₃ are not coplanar; and wherein said waves S₁, S₂, S₃, R₁, R₂, and R₃have the same wavelength, i) illuminating said holographic medium withsaid third signal wave S₃ and said third reference wave R₃, therebyrecording a third grating in said medium, j) illuminating saidholographic medium with said first reference wave R₁, thereby generatingfirst, second, and third reconstructed waves characterized by first,second, and third reconstructed wave vectors, respectively, wherein saidfirst reconstructed wave vector is equal to said first signal wavevector σ₁, said second reconstructed wave vector is equal to thenegative of said second reference wave vector ρ₂, and said thirdreconstructed wave vector is equal to the negative of said thirdreference wave vector ρ₃.
 8. The method of claim 7, further comprisingthe step of projecting said first, second and third reconstructed waveson an imaging means.
 9. The method of claim 7, further comprising thefollowing steps:a) projecting said first reconstructed wave onto animaging means, and b) positioning said imaging means so that said secondreconstructed wave does not intercept said imaging means.
 10. The methodof claim 7, wherein said first, second, and third signal waves S₁, S₂and S₃ are impressed with digital data.
 11. The method of claim 7,wherein said first, second, and third signal waves S₁, S₂, and S₃ areimpressed with analog data.